removing every other node in tree

[HG319]

Given a bst how can you remove every other node in the tree

Here is the code for removing one node in the tree and also deleting the whole tree. how can i modify one of these to make it remove every other

void remove( const Comparable & x, BinaryNode * & t )
    {
        if( t == nullptr )
            return;   // Item not found; do nothing
        if( x < t->element )
            remove( x, t->left );
        else if( t->element < x )
            remove( x, t->right );
        else if( t->left != nullptr && t->right != nullptr ) // Two children
        {
            t->element = findMin( t->right )->element;
            remove( t->element, t->right );
        }
        else
        {
            BinaryNode *oldNode = t;
            t = ( t->left != nullptr ) ? t->left : t->right;
            delete oldNode;
        }
    }

void makeEmpty( BinaryNode * & t )
    {
        if( t != nullptr )
        {
            makeEmpty( t->left );
            makeEmpty( t->right );
            delete t;
        }
        t = nullptr;
    }